We have proposed a method for estimating the instantaneous epipole from uncalibrated optical flow containing a single rigid motion. Our experiments indicate that the method works with very good reliability. In this section we discuss briefly differences and similarities with the related techniques that we regard as most directly relevant, then sketch the directions of current and future research.
Heeger and Jepson [ 5 ] proposed a method that uses a least-squares residual function to determine the direction of translation, but is inherently based on the knowledge of the intrinsic parameters (all equations are written in camera, not screen, coordinates). It is well-known that this knowledge is not necessary for finding the epipole [ 2 ] and our method does not make use of it. Moreover, [ 5 ] concentrates on 3-D motion and reconstruction, and do not discuss the structure of the optical flow equations derived. An advantage of [ 5 ] is that their search space is limited to the unit sphere, whereas, in our case, the search space is the whole image plane. As theirs, our method is conceptually simple and embeds a natural parallel structure ( e.g. , the computation could take place at all the points used simultaneously).
The method proposed by Rieger and Lawton [ 10 ] is based on the notion of motion parallax, and needs therefore good flow estimates at locations with large depth variation. This is a strong hypothesis which seems to jeopardize the general applicability of the method. Again, the intrinsic parameters are assumed known. Interestingly, Rieger and Lawton point out the relevance of their results for human motion perception, most of which apply to our work as well.
The research reported in this paper has started a number of promising spin-offs and developments. We are pursuing a thorough theoretical understanding of the robustness of the method, as well as of the inherent ambiguity of uncalibrated optical flows in terms of 3-D motion and structure. We are planning experiments on real sequences accompanied by ground truth. We have also begun to investigate the practical use and estimation of the generalized time-to-impact, and the relation with psychophysics for the recovery of heading.
This work was supported by EPSRC Visiting Fellowship GR/L18716.
Adrian F Clark